3.30 Measurements of scientific systems are alwayssubject to variation, some more than others. Thereare many structures for measurement error, and statis-ticians spend a great deal of time modeling these errors.Suppose the measurement error X of a certain physicalquantity is decided by the density function[k(3-x²),f(x) =10,(a) Determine k that renders f(x) a valid density func-tion.(b) Find the probability that a random error in mea-surement is less than 1/2.−1≤x≤1,elsewhere.(c) For this particular measurement, it is undesirableif the magnitude of the error (i.e., |x|) exceeds 0.8.What is the probability that this occurs?

Given that Probability density functions of X is f(x) = k(3 - x2) , -1 < X < 1

Answered: (a) Determine k that renders f(x) a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Let X be exponentially distributed with parameter λ. Calculate the probability density of Y =(X−3)/(X+1). please provide some explanation with the taken steps, thank you in advance.
Find the mean, standard deviation and the median of the density function: f(x)= (6/343)x(7-x) [0,7]
Consider the probability density function if x 5. Find Pr(X < ) (accurate to 4 decimal places). Select one: O 0.7803 O 0.2603 O 0.9897 O 0.2197
(f) | For each of the following families of distributions, explain whether it is an exponential family: Bernoulli(p), p € (0, 1) Ν (μ. 1), μER N (µ, o²), µ E R and o² > 0 Exponential(A), ^ > 0
A continuous random variable has the probability density function of f(x)=0.0118x and the interval of [O 13]. What is the probability that this variable has a value between 1 and 2? Answer: A continuous random variable has the probability density function of f(x)=0.0118x and the interval of [O 13]. What is the cumulative distribution function for the value of 3? Answer:
EX#1: Let the continuous random variable X denote the current measured in a wire in milliamperes. Assume that the range of X is [4.9,5.1] mA, and assume that the probability density function of X is f (x) = 5 for 4.9 < x < 5.1. What is the probability that a current measurement is less than 5 mA?
For the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the random variable x is within one standard deviation of the mean. f(x) = 195x, (0,5] 2, [0,5] 125 a) Find the mean. (Round to three decimal places as needed.) b) Find the standard deviation. O = (Round to three decimal places as needed.) c) Find the probability that the random variable x is within one standard deviation of the mean. The probability is. (Round to three decimal places as needed.)
According to a study, the maximum temperature T (in degrees Celsius) of each day during the spring has a distribution with the following function density: 21
4) It has been determined that the probability density function for the wait in line at a counter is given by, So f(t) = if t 0 a) Verify that this is in fact a probability density function. b) Determine the probability that a person will wait in line for at least 6 minutes. c) Determine the mean wait in line.

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

(a) Determine k that renders f(x) a valid density func- tion. (b) Find the probability that a random error in mea- surement is less than 1/2. (c) For this particular measurement, it is undesirable if the magnitude of the error (i.e., [x]) exceeds 0.8. What is the probability that this occurs?